Yet Another XOR Problem

You are given two integer arrays $A$ and $B$ of length $N$.

You may perform the following operation on array $A$ any number of times.

Choose an integer $i$ such that $2 \leq i \leq N-1$. Then replace $A_i$ with $A_{i-1} \oplus A_i \oplus A_{i+1}$, where $\oplus$ denotes bitwise XOR.

Determine whether array $A$ can be made equal to array $B$.

The input is given in the following format.

$T$ $N$ $A_1\ A_2\ \cdots\ A_N$ $B_1\ B_2\ \cdots\ B_N$ $\vdots$

The first line contains the number of test cases $T$. Each test case consists of $N$, array $A$, and array $B$ in this order.

For each test case, print YES if array $A$ can be made equal to array $B$, and print NO otherwise.

• $1 \leq T \leq 5\ 000$.
• $3 \leq N \leq 200\ 000$.
• $0 \leq A_i, B_i < 2^{30}$ ($1 \leq i \leq N$).
• The sum of $N$ over all test cases does not exceed $200\ 000$.